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one approved set of solar tables, converted into time at the rate of 360° to the tropical year. Its unit is the mean tropical year which those tables assume and no other, and its epoch is the mean vernal equinox of these tables for the current year, or the instant when the mean longitude of the tables is rigorously 0, according to the assumed mean motion of the sun and equinox, the assumed epoch of mean longitude, and the assumed equinoctial point on which the tables have been computed, and no other. To give complete effect to this idea, it only remains to specify the particular tables fixed upon for the purpose, which ought to be of great and admitted excellence, since, once decided on, the very essence of the conception is that no subsequent alteration in any respect shoulU be made, even when the continual progress of astronomical science shall have shown any one or all of the elements concerned to be in some minute degree erroneous (as necessarily they must), and shall have even ascertained the corrections they require (to be themselves again corrected, when another step in refinement shall have been made).

(937.) Delambre's solar tables (in 1828) when this mode of reckoning time was first introduced, appeared entitled to this distinction. According to these tables, the sun's mean longitude was 0°, or the mean vernal equinox occurred, in the year 1828, on»the 22d of March at lh 2m 59*-05 mean time at Greenwich, and therefore at lh 12m 20,-55 mean time at Paris, or lh 56m 34»-55 mean time at Berlin, at which instant, therefore, the equinoctial time was 0d & 0TM 0"-00, being the commencement of the 1828th year current of equinoctial time, if we choose to date from the mean tabular equinox, nearest to the vulgar era, or of the 6541st year of the Julian period, if we prefer that of the first year of that period.

(938.) Equinoctial time then dates from the mean vernal equinox of Delambre's solar tables, and its unit is the mean tropical year of these tables (365d-242264). Hence, having the fractional part of a day expressing the difference between the mean local time at any place (suppose Greenwich) on any one day between two consecutive mean vernal equinoxes that difference will be the same for every other day in the

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same Interval Thus, between the mean equinoxes of 1828 and 1829, the difference between equinoctial and Greenwich time is 0d-956261 or 0<- 22h 57m 0'-95, which expresses the equinoctial day, hour, minute, and second, corresponding to mean noon at Greenwich on March 23. 1828, and for the noons of the 24th, 25th, &c, we have only to substitute Id, 2d, &c. for 0d, retaining the same decimals of a day, or the same hours, minutes, &c, up to and including March 22. 1829. Between Greenwich noon of the 22d and 23d of March, 1829, the 1828th equinoctial year terminates, and the 1829th commences. This happens at O^SGOOS, or at 6h 51m 50*-66 Greenwich mean time, after which hour, and until the next noon, the Greenwich hour added to equinoctial time 364d-956261 will amount to more than 365-242264, a complete year, which has therefore to be subtracted to get the equinoctial date in the next year, corresponding to the Greenwich time. For example, at 12h 0TM 0* Greenwich mean time, or 0d,500000, the equinoctial time will be 364-956261+0-500000 = 365-456261, which being greater than 365*242264, shows that the equinoctial year current has changed, and the latter number being subtracted, we get 0---213977 for the equinoctial time of the 1829th year current corresponding to March 22., 12h Greenwich mean time.

(939.) Having, therefore, the fractional part of a day for any one year expressing the equinoctial hour, &c, at the mean noon of any given place, that for succeeding years will be had by subtracting 0d-242264, and its multiples, from such fractional part (increased if necessary by unity), and for preceding years by adding them. Thus, having found 0-19852* for the fractional part for 1827, we find for the fractional parts for succeeding years up to 1853 as follows*: —

* These numbers differ from those in the Nautical Almanack, and woul require to be substituted for them, to carry out the idea of equinoctial time as above laid down. In the years 1828—1833, the late eminent editor of that work used an equinox slightly differing from that of Delambre, which accounts for the difference in those years. In 1834, it would appear that a deviation both from the principle of the text and from the previous practice of that ephemeris took place, in deriving the fraction for 1834 from that for 1833, which has been ever since perpetuated. It consisted in rejecting the mean longitude of Delambrc's tables, and adopting Besscl's correction of that clement. The effect

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of this alteration was to insert 3m 3B*68 of purely imaginary time, between the end of the equinoctial year 1833 and the beginning of 1834, or, in other wor.lv to make the interval between the noons of March 22. and 23. 1834, 24b 3° 3"-68, when reckoned by equinoctial time. In 1835, and in all subsequent years, i further departure from the principle of the text took place by substituting Bessel'i tropical year of 365*2422175, for Delambre's. Thus the whole subject hu fallen into confusion.

[kote on Art. 932.

The reformation of Gregory was, after all, incomplete. Instead of 10 daji he ought to have omitted 12. The interval from Jan. 1. A. S. I, to Jan. 1. *.». 1582, reckoned as Julian years, is 577460 days, and as tropical, 577448, with an error not exceeding 0^*01, the difference being 12 days, whose omission would have completely restored the Julian epoch. But Gregory assumed foi his fixed point of departure, not that epoch, but one later by 324 years, vis. Jan. 1. A. D. 325, the year of the Council of Nice; assuming which, the difference of the two reckonings is 9* 505, or, to the nearest whole number, 10 days.]

APPENDIX.
I. ListS OF NORTHERN AND SOUTHERN STARS, WITH THEIR APPROXIMATE MAGNITUDES, ON

THE VULGAR AND PHOTOMETRIC SCALE.

1. NORTHERN STARS.

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of this alteration was to insert 3m 3*68 of purely imaginary time, between the end of the equinoctial year 1833 and the beginning of 1834, or, in other words to make the interval between the noons of March 22. and 23. 1834, 24" S" 3*-68, when reckoned by equinoctial time. In 1835, and in all subsequent years, i further departure from the principle of the text took place by substituting Bessel's tropical year of S65-2422175, for Delambre's. Thus the whole subject has fallen into confusion. >

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[Note on Art. 932.

The reformation of Gregory was, after all, incomplete. Instead of 10 daw he ought to have omitted 12. The interval from Jan. 1. A. D. 1, to Jan. 1. *. n, 1582, reckoned as Julian years, is 577460 days, and as tropical, 577448, with an error not exceeding O^'Ol, the difference being 12 days, whose omission would have completely restored the Julian epoch. But Gregory assumed for his fixed point of departure, not that epoch, but one later by 324 years, via. Jan. 1. A.i). 325, the year of the Council of Nice; assuming which, the difference of the two reckonings is 9J\505, or, to the pearest whole number, 10 days.]

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